(1.7 hours to learn)
Vector spaces are spaces which are closed under addition and scalar multiplication. Examples include vectors, matrices, polynomials, and functions. Many core concepts of linear algebra, such as linear independence, bases, and dimension, are defined for general vector spaces.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ A First Course in Linear Algebra (2012)
A linear algebra textbook with proofs.
→ Linear Algebra Done Right
A textbook for a second course in linear algebra, with mathematical generalizations of the basic concepts.
Location: Chapter 1, "Vector spaces," subsections "Definition of vector space" and "Properties of vector space," pages 4-12
Supplemental resources (the following are optional, but you may find them useful)
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 3.1, "Spaces of vectors," up to "Subspaces," pages 120-121
-No Additional Notes-
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation